Low tubal rank tensor completion based on singular value factors

Abstract

Inspired by the definition of tensor-tensor product and tensor tubal rank, a randomized singular value decomposition of tensor is presented in this paper. Based on tensor singular value decomposition (t-SVD) and tensor randomized singular value decomposition (t-RSVD), we obtain two efficient algorithms to solve tensor completion problem. We also propose the adaptive rank method to adjust the tubal rank of tensor. The main advantage of the random projection-based t-RSVD is to cut down the computing time in consideration of large-scale problems. In the optimization process, the alternating minimization algorithm is employed to solve the tensor completion problem. Finally, numerical experiment results indicate that the t-RSVD is competitive and consumes less time than the t-SVD. The efficiency and feasibility of our methods are illustrated by the image and video recovery.

Keywords:

• Tensor completion
• random projection
• randomized algorithms
• tubal rank
• discrete Fourier transformation
• tensor randomized singular value Decomposition

AMS subject classifications:

• 15A18
• 15A69
• 65F10

Acknowledgments

The authors would like to thank the anonymous referees and the editor for their very detailed comments and suggestions, which greatly improved the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 https://pixabay.com.

2 https://tv.cctv.com/lm/xwlb/index.shtml.

Additional information

Funding

This research is supported by the National Natural Science Foundation of China [grant number 11971294] and Doctoral Research Fund of Nantong University [grant number 135420602001].